a(n) = F(n+1) + c(n) where F(k) is k-th Fibonacci number and c(n) is n-th non-Fibonacci number.

Terms

a(0) =5a(1) =8a(2) =10a(3) =14a(4) =18a(5) =24a(6) =33a(7) =48a(8) =70a(9) =105a(10) =161a(11) =251a(12) =396a(13) =630a(14) =1009a(15) =1620a(16) =2608a(17) =4206a(18) =6791a(19) =10973a(20) =17739a(21) =28686a(22) =46398a(23) =75056a(24) =121425a(25) =196451a(26) =317846a(27) =514265a(28) =832077a(29) =1346307